Page 421 - DMTH404_STATISTICS

Sachin Kaushal, Lovely Professional University Unit 31: Hypothesis Testing

Unit 31: Hypothesis Testing Notes

CONTENTS

Objectives
Introduction
31.1 Test of Hypothesis
31.2 Tests of Hypothesis Concerning Mean

31.2.1 Test of Hypothesis Concerning Population Mean (s being known)
31.2.2 Test of Hypothesis Concerning Population Mean (s being unknown)
31.2.3 Test of Hypothesis Concerning Equality of two Population Means
31.2.4 Paired t - Test

31.3 Tests of Hypothesis concerning Proportion
31.3.1 Test of Hypothesis that Population Proportion is p0
31.3.2 Test of Hypothesis Concerning Equality of Proportions
31.5 Summary

31.6 Keywords
31.7 Self Assessment
31.8 Review Questions
31.9 Further Readings

Objectives

After studying this unit, you will be able to:
 Discuss Hypothesis Testing

 Explain Hypothesis Concerning Mean
Introduction

A hypothesis is a preconceived idea about the nature of a population or about the value of its
parameters. The statements like the distribution of heights of students of a university is normally
distributed, the number of road accidents per day in Delhi is 10, etc., are some examples of a
hypothesis.
The test of a hypothesis is a procedure by which we test the validity of a given statement about
a population. This is done on the basis of a random sample drawn from it.
The hypothesis to be tested is termed as Null Hypothesis, denoted by H . This hypothesis asserts
0
that there is no difference between population and sample in the matter under consideration.
For example, if H is that population mean  =  , then we regard the random sample to have
0 0
been obtained from a population with mean m .
0
Corresponding to any H , we always define an Alternative Hypothesis. This hypothesis, denoted
0
by H , is alternate to H , i.e., if H is false then H is true and vice-versa.
a 0 0 a
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